Proposition 3.1 (Feynman-Kac formula, [1]}) 
Under the assumptions of Section , the (unique)
non-negative solution \(u\)  to (REF ) is given by
\(u(t,x) = E_x \Big [\exp \Big \lbrace  \int _0^t \xi (B_s) \, {\rm d}s \Big \rbrace \, u_0(B_t) \Big ],\) 
